Hans Troger, TU Wien (Koautoren: M.Matzl, W.Poth, A.Steindl, G.Wiedermann)
The dynamics of tethered satellite systems, that is an arrangement of two or more satellites, which are connected by thin long cables in orbit around a planet, is described by a coupled set of nonlinear ordinary and partial differential equations. We present the equations in weak form, which for the system of varying mass composition is nontrivial. Since the equations are stiff their numerical treatment requires special measures. One possibility is to introduce an alternative set of variables (natural string variables) for the description of the deformation of the tether. In these new variables the equations, to some extend, decouple with respect to the slow and fast motions. The discretization of the tether in space is performed by Finite Elements and by Finite Differences. Two different formulations of the equations of motion and various time integrators, especially qualified for stiff systems, are compared with each other. With the developed computer code some selected (partly animated) simulation results concerning practically important motions of the tethered satellite system, both with constant and variable tether length, and applying control will be presented.